Haseman and Elston (1972) introduced a sib-pair method using classical regression analysis to detect linkage between a polymorphic marker locus and a quantitative trait locus without assuming a specific genetic model for the quantitative trait. This method has been extended to allow for multiple traits (multivariate) and multiple marker loci (multipoint). Here we are investigating the extension to multiple trait loci (multilocal). In particular, we consider the case of two unlinked quantitative trait loci each linked to one of two unlinked polymorphic marker loci. For a two-locus epistatic model, we have devised a general formulation of the complete regression model and details of the regression coefficients in terms of variance components. This research is relevant to complex binary disease traits, which, without loss of generality, can be viewed as quantitative traits taking on the two values 0 (unaffected) and 1 (affected).